94-20 Baladi V.

Infinite kneading matrices and weighted zeta functions of interval maps (52K, AMS TeX) Jan 23, 94

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Abstract. We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coefficients analytic functions. We show that the determinant of this infinite matrix is the inverse of the correspondingly weighted zeta function for the map. As a corollary, we obtain convergence of the discrete spectrum of the Perron-Frobenius operators of piecewise linear approximations of Markovian, piecewise expanding and piecewise $C^{1+BV}$ interval maps. (This is a revised version of the paper sent in December 1993.)

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